Re: Simple yet Profound Metatheorem

In article <1134713007.253164.75100@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
"sradhakr" <sradhakr@xxxxxxxxxx> wrote:

>Barb Knox wrote:
>
>> If you want provability and truth to be the same, you can dispense with
>> all the modal machinery and just use some existing well-thought-out
>> constructive logic (e.g. Intuitionistic).
>>
>False. Truth and provability are *not* the same in
>intuitionistic/constructive logics. If you claim otherwise, show me a
>valid proof of the law of non-contradiction i.e., of ~(P&~P), in these
>logics.

OK, here's a Fitch-style Intuitionistic ND proof:

1. | P ^ ~P A
|-------
2. | P 1 ^E
3. | ~P 1 ^E
4. ~(P ^ ~P) 1,2,3 RAA


>Any "proof" of ~(P&~P) that you produce from contradictory
>premises is not a valid proof in these logics.

Eh? I've given a perfectly valid Intuitionistic proof. On what grounds
do you object to it (if you do)?

[snip]

--
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| BBB b \ Barbara at LivingHistory stop co stop uk
| B B aa rrr b |
| BBB a a r bbb | Quidquid latine dictum sit,
| B B a a r b b | altum viditur.
| BBB aa a r bbb |
-----------------------------
.

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